MAT 142 Basic Calculus II, Spring 2023-2024
Question Set #1
Q 1. Evaluate the indefinite integral
Z
Q 2. Evaluate the indefinite integral
Z
9
dx
x ln 5x
7 sec2 x tan x dx
Q 3. Evaluate the indefinite integral
Z
p
y 4 y + 5 dy
Q 4. Evaluate the definite integral.
Z 4
2
1
dx
2x − 3
Q 5. Evaluate the definite integral
Z π/3
0
−5 sin x
dx
cos2 x
Q 6. Evaluate the indefinite integral
Z
x
dx
16 + x4
Q 7. Evaluate the indefinite integral
Z
t cos3 (t2 ) dt
Q 8. Sketch the region enclosed by the given curves y = 6x2 and y = x2 + 5. Decide whether
to integrate with respect to x or y. Then find the area of the region.
Q 9. Find the area of the region enclosed between f (x) = x2 + 4x and g(x) = 2x2 + 3x − 2.
1
Q 10. Find the area of the shaded region below
2